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A269549
Expansion of (-x^2 + 298*x - 1)/(x^3 - 99*x^2 + 99*x - 1).
8
1, -199, -19799, -1940399, -190139599, -18631740599, -1825720439399, -178901971320799, -17530567468999199, -1717816709990600999, -168328507011609898999, -16494475870427779501199, -1616290306794910781218799, -158379955590030828779941399, -15519619357516226309653038599
OFFSET
0,2
COMMENTS
Mc Laughlin (2010) gives an identity relating ten sequences, denoted a_k, b_k, ..., f_k, p_k, q_k, r_k, s_k. This is the sequence c_k.
FORMULA
G.f.: (-x^2 + 298*x - 1)/(x^3 - 99*x^2 + 99*x - 1).
a(n) = 37/12 + ((2*sqrt(6) - 5)/(2*sqrt(6) + 5)^(2*n) - (2*sqrt(6) + 5)*(2*sqrt(6) + 5)^(2*n))*5/24. - Bruno Berselli, Mar 01 2016
MATHEMATICA
CoefficientList[Series[(-x^2 + 298 x - 1)/(x^3 - 99 x^2 + 99 x - 1), {x, 0, 20}], x] (* or *) Table[FullSimplify[37/12 + ((2 Sqrt[6] - 5)/(2 Sqrt[6] + 5)^(2 n) - (2 Sqrt[6] + 5) (2 Sqrt[6] + 5)^(2 n)) 5/24], {n, 0, 20}] (* Bruno Berselli, Mar 01 2016 *)
PROG
(PARI) Vec((-x^2 + 298*x - 1)/(x^3 - 99*x^2 + 99*x - 1) + O(x^20))
(Sage)
gf = (-x^2+298*x-1)/(x^3-99*x^2+99*x-1)
print(taylor(gf, x, 0, 20).list()) # Bruno Berselli, Mar 01 2016
(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((-x^2+298*x-1)/(x^3-99*x^2+99*x-1))); // Bruno Berselli, Mar 01 2016
KEYWORD
sign,easy
AUTHOR
Michel Marcus, Feb 29 2016
STATUS
approved